The first time I heard of Clara Barton was when I was around 10 years old and took a book out of the library containing short biographies of famous American women.

38A. Clearance sites? Answer: Throats. A nifty play on words, don’t you think?
57A. Capital of the country that’s alphabetically first in the United Nations. Answer: Kabul. So, that would be Afghanistan.
60A. The Battle Born State: Abbr. Answer: Nev. Didn’t know this was Nevada’s nickname.

The lower right quadrant gave me the most difficulty and was the last to be filled in.

42A. Vocabulary-related. Answer: Lexical. As a former English teacher, I don’t know why this stumped me. But it did. I had the last 4 letters but had trouble coming up with the first three. When the answer finally dawned on me, it led to being able to fill in the rest of the quadrant.

44D. Abnormal dryness to a dermatologist. Answer: Xerosis. The “x” is also the “x” in “lexical.” If I hadn’t gotten that answer, I’d never have gotten this one since I’ve never heard this medical term before.